Foreword xi
Preface xiii
Acknowledgments xvii
Acronyms xix
Introduction xxi

1 Transfer Matrix Approach 1
1.1 Generalized Rectangular Barrier 1
1.2 MacColl–Hartman Effect 5
1.3 Plane Wave TMA 11
1.4 Airy TMA 19
1.5 Fowler–Nordheim Tunneling 24
1.6 Kemble Approximation 28
1.7 Reflectionless Versus Resonant 32
1.8 Exercises 37

2 Schrödinger Approach 39
2.1 Quantum Carpets 39
2.2 Wave Packets 40
2.3 Triangular Barriers 47
2.4 Exercises 50

3 Wigner Approach 51
3.1 Wave Packets (Again) 51
3.2 Time Evolution 56
3.3 Wells 66
3.4 Exercises 74

4 Emission 77
4.1 Notional Emission Area 77
4.1.1 Hemisphere 77
4.1.2 Hyperboloid 80
4.1.3 Ellipsoid 82
4.2 Launch Velocity 83
4.3 Ballistic Impulse Model 86
4.4 Emittance 95
4.4.1 Thermal Emission Emittance 99
4.4.2 Photoemission Emittance 99
4.4.3 Field Emission Emittance 100
4.5 Beam Envelope Equation 101
4.6 Schottky's Conjecture 106
4.7 Conical Point Charge Model 110
4.8 Boundary Element Methods 116
4.9 Exercises 118

5 Shape 121
5.1 Wire and Nanotube Emitters 122
5.2 Hemisphere Current 129
5.3 Nanotip Barriers 136
5.4 Tip Space Charge 139
5.5 Emitter Statistics 143
5.6 Exercises 151

6 Materials 153
6.1 Thermally Assisted Photoemission 153
6.2 Moments Model Augmentation 159
6.3 Optical Terms 161
6.3.1 Metals 161
6.3.2 Semiconductors 168
6.4 Effective Mass and DOS 173
6.5 Scattering Models 175
6.6 Numerical QE Model 179
6.7 Exercises 180

7 Coatings 183
7.1 Evaporation and Diffusion 183
7.2 Pores and Lifetime 191
7.3 Work Function Reduction 198
7.4 Exercises 209

8 Conclusion 213

A Constants and Functions 215
A.1 Units and Fundamental Constants 215
A.2 Optical Constants 216
A.3 Airy Functions 217
A.4 Error Functions 218
A.5 Psi Function 219
A.6 Forbes–Deane Approximation 220
A.7 Elliptical Integrals 221Contents ix

B Algorithms 223
B.1 General Algorithms 223
B.1.1 FUNdamental 223
B.1.2 QPlot 224
B.1.3 CPlot 226
B.2 TMA Algorithms 226
B.2.1 Airy Function Approximations 226
B.2.2 Planar and Airy TMA 229
B.2.3 MacColl–Hartman Effect 238
B.2.4 Sech-squared Well 240
B.3 Schrödinger Algorithms 242
B.3.1 Quantum Carpets 242
B.3.2 Plane Wave Packets 244
B.3.3 Airy Wave Packets 249
B.4 Wigner Algorithms 253
B.4.1 Gaussian Wave Packet, Ballistic 253
B.4.2 Gaussian Wave Packet, WDF 254
B.4.3 Wigner in a Well 257
B.5 Structure 259
B.5.1 Notional Emission Area 259
B.5.2 Launch Velocity 260
B.5.3 Beam Radius 261
B.5.4 Schottky's Conjecture 263
B.5.5 Conical Point Charge Model 265
B.5.6 Hot Carbon Fiber 268
B.5.7 Heating of Carbon Cone 270
B.5.8 Statistics and Degradation 271
B.6 Materials 276
B.6.1 Thermal Modified Photoemission 276
B.6.2 Optical LDR Models: Metal 278
B.6.3 Optical ADR Models: Semiconductor 284
B.6.4 Rapid Photoemission Model 289
B.7 Coatings 293
B.7.1 Lattice Diffusion Model 293
B.7.2 Knudsen Flow 296
B.7.3 Modified Gyftopoulos-Levine Model 299
B.7.4 Coverage and QE 302

References 305
Index 341